You may want to consider getting the criminal conviction removed/expunged from your record. The waiting period prior to application will depend on your country.
You'll be fine, don't worry about it. If you need peace of mind, book a dummy ticket from an onward ticket website. For stamp extention you may need to wait until 45 or 30 days remaining instead of doing it immediately.
Not sure if "need" to. But probably should provide confirmation of business/tax registration. Most people report submitting it. But if you reply without it and the embassy wants it, they'll ask for further documents. Of course, this will extend the process.
As for other documents (not mentioned in your post), I would draft a cover letter briefly explaining your business, self-employed status, and remote nature of the work.
Regarding proof of location, you'll want to provide both entry/visa stamp and proof of accomodation (e.g. booking confirmation)
reason to get the visa is if you already have a recent history of a lot of visa exemptions, and it seems you're trying to live in Thailand off them, as many immigration officers have been "cracking down" more recently